Measure Rigidity in Higher Rank Lattice Actions - 1/3

Explore the fundamental concepts of measure rigidity in higher rank lattice actions through this comprehensive mathematical lecture delivered at the Institut des Hautes Etudes Scientifiques. Begin by examining essential definitions and properties related to higher rank lattice actions, then delve into the crucial role that measures and measure rigidity play across various mathematical settings. Learn how measure rigidity serves as a powerful tool for understanding classical theorems, including Margulis' normal subgroup theorem and Margulis' superrigidity theorem. Discover recent developments in the field through an exploration of smooth actions of higher rank lattices on manifolds, particularly within the framework of the Zimmer program. Gain insights into how these theoretical concepts connect to broader mathematical research and applications in the study of lattice actions and their geometric properties.